



'''simple docstring'''





import copy
import re






class __A     :



 '''simple docstring'''







 __lowerCamelCase       :			List[Any]		=			'hp'
 __lowerCamelCase       :			str		=			{}
 __lowerCamelCase       :			Tuple		=			None



 @classmethod
 def    a__    (cls					,  A					,  A			)       ->	int:


      """simple docstring"""



      _a           =    prefix
      _a           =    defaults
      cls.build_naming_info()



 @staticmethod
 def    a__    (A					,  A			)       ->	Union[str, Any]:


      """simple docstring"""



      if len(A			) == 0:
           return ""
      _a           =    None
      if any(char.isdigit() for char in word			):
           raise Exception(f'''Parameters should not contain numbers: \'{word}\' contains a number'''			)
      if word in info["short_word"]:
           return info["short_word"][word]
      for prefix_len in range(1					,  len(A			) + 1			):
           _a           =    word[:prefix_len]
           if prefix in info["reverse_short_word"]:
                continue
           else:
                _a           =    prefix
                break

      if short_word is None:
           # Paranoid fallback
           def int_to_alphabetic(A			):
                _a           =    ''''''
                while integer != 0:
                     _a           =    chr(ord('''A'''			) + integer % 10			) + s
                     integer //= 10
                return s

           _a           =    0
           while True:
                _a           =    word + '''#''' + int_to_alphabetic(A			)
                if sword in info["reverse_short_word"]:
                     continue
                else:
                     _a           =    sword
                     break

      _a           =    short_word
      _a           =    word
      return short_word



 @staticmethod
 def    a__    (A					,  A			)       ->	Optional[int]:


      """simple docstring"""



      _a           =    param_name.split('''_'''			)

      _a           =    [TrialShortNamer.shortname_for_word(A					,  A			) for word in words]

      # We try to create a separatorless short name, but if there is a collision we have to fallback
      # to a separated short name
      _a           =    ['''''', '''_''']

      for separator in separators:
           _a           =    separator.join(A			)
           if shortname not in info["reverse_short_param"]:
                _a           =    shortname
                _a           =    param_name
                return shortname

      return param_name



 @staticmethod
 def    a__    (A					,  A			)       ->	Optional[Any]:


      """simple docstring"""



      _a           =    TrialShortNamer.shortname_for_key(A					,  A			)
      _a           =    short_name
      _a           =    param_name



 @classmethod
 def    a__    (cls			)       ->	Dict:


      """simple docstring"""



      if cls.NAMING_INFO is not None:
           return

      _a           =    {
          '''short_word''': {},
          '''reverse_short_word''': {},
          '''short_param''': {},
          '''reverse_short_param''': {},
      }

      _a           =    list(cls.DEFAULTS.keys()			)

      for k in field_keys:
           cls.add_new_param_name(A					,  A			)

      _a           =    info



 @classmethod
 def    a__    (cls					,  A			)       ->	Tuple:


      """simple docstring"""



      cls.build_naming_info()
      assert cls.PREFIX is not None
      _a           =    [copy.copy(cls.PREFIX			)]

      for k, v in params.items():
           if k not in cls.DEFAULTS:
                raise Exception(f'''You should provide a default value for the param name {k} with value {v}'''			)
           if v == cls.DEFAULTS[k]:
                # The default value is not added to the name
                continue

           _a           =    cls.NAMING_INFO['''short_param'''][k]

           if isinstance(A					,  A			):
                _a           =    1 if v else 0

           _a           =    '''''' if isinstance(A					,  (int, float)			) else '''-'''
           _a           =    f'''{key}{sep}{v}'''
           name.append(A			)

      return "_".join(A			)



 @classmethod
 def    a__    (cls					,  A			)       ->	List[Any]:


      """simple docstring"""



      _a           =    repr[len(cls.PREFIX			) + 1 :]
      if repr == "":
           _a           =    []
      else:
           _a           =    repr.split('''_'''			)

      _a           =    {}

      for value in values:
           if "-" in value:
                _a    ,       _a           =    value.split('''-'''			)
           else:
                _a           =    re.sub('''[0-9.]'''					,  ''''''					,  A			)
                _a           =    float(re.sub('''[^0-9.]'''					,  ''''''					,  A			)			)

           _a           =    cls.NAMING_INFO['''reverse_short_param'''][p_k]

           _a           =    p_v

      for k in cls.DEFAULTS:
           if k not in parameters:
                _a           =    cls.DEFAULTS[k]

      return parameters





"""simple docstring"""


import numpy as np



def 						lowerCamelCase__      (				UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_ = 1E-12		,   UpperCAmelCase_ = 1_00		,   )->				tuple[float, np.ndarray]:







       """simple docstring"""
       assert np.shape(UpperCAmelCase_					)[0] == np.shape(UpperCAmelCase_					)[1]
       # Ensure proper dimensionality.
       assert np.shape(UpperCAmelCase_					)[0] == np.shape(UpperCAmelCase_					)[0]
       # Ensure inputs are either both complex or both real
       assert np.iscomplexobj(UpperCAmelCase_					) == np.iscomplexobj(UpperCAmelCase_					)
       UpperCamelCase       			=		np.iscomplexobj(UpperCAmelCase_					)
       if is_complex:
              # Ensure complex input_matrix is Hermitian
              assert np.array_equal(UpperCAmelCase_		,   input_matrix.conj().T					)

       # Set convergence to False. Will define convergence when we exceed max_iterations
       # or when we have small changes from one iteration to next.

       UpperCamelCase       			=		False
       UpperCamelCase       			=		0
       UpperCamelCase       			=		0
       UpperCamelCase       			=		1E12

       while not convergence:
              # Multiple matrix by the vector.
              UpperCamelCase       			=		np.dot(UpperCAmelCase_		,   UpperCAmelCase_					)
              # Normalize the resulting output vector.
              UpperCamelCase       			=		w / np.linalg.norm(UpperCAmelCase_					)
              # Find rayleigh quotient
              # (faster than usual b/c we know vector is normalized already)
              UpperCamelCase       			=		vector.conj().T if is_complex else vector.T
              UpperCamelCase       			=		np.dot(UpperCAmelCase_		,   np.dot(UpperCAmelCase_		,   UpperCAmelCase_					)					)

              # Check convergence.
              UpperCamelCase       			=		np.abs(lambda_ - lambda_previous					) / lambda_
              iterations += 1

              if error <= error_tol or iterations >= max_iterations:
                     UpperCamelCase       			=		True

              UpperCamelCase       			=		lambda_

       if is_complex:
              UpperCamelCase       			=		np.real(lambda_					)

       return lambda_, vector



def 						lowerCamelCase__      (				)->				None:







       """simple docstring"""
       UpperCamelCase       			=		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]					)
       UpperCamelCase       			=		np.array([41, 4, 20]					)
       UpperCamelCase       			=		real_input_matrix.astype(np.complexaaa					)
       UpperCamelCase       			=		np.triu(1j * complex_input_matrix		,   1					)
       complex_input_matrix += imag_matrix
       complex_input_matrix += -1 * imag_matrix.T
       UpperCamelCase       			=		np.array([41, 4, 20]					).astype(np.complexaaa					)

       for problem_type in ["real", "complex"]:
              if problem_type == "real":
                     UpperCamelCase       			=		real_input_matrix
                     UpperCamelCase       			=		real_vector
              elif problem_type == "complex":
                     UpperCamelCase       			=		complex_input_matrix
                     UpperCamelCase       			=		complex_vector

              # Our implementation.
              UpperCamelCase			,							UpperCamelCase       			=		power_iteration(UpperCAmelCase_		,   UpperCAmelCase_					)

              # Numpy implementation.

              # Get eigenvalues and eigenvectors using built-in numpy
              # eigh (eigh used for symmetric or hermetian matrices).
              UpperCamelCase			,							UpperCamelCase       			=		np.linalg.eigh(UpperCAmelCase_					)
              # Last eigenvalue is the maximum one.
              UpperCamelCase       			=		eigen_values[-1]
              # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
              UpperCamelCase       			=		eigen_vectors[:, -1]

              # Check our implementation and numpy gives close answers.
              assert np.abs(eigen_value - eigen_value_max					) <= 1E-6
              # Take absolute values element wise of each eigenvector.
              # as they are only unique to a minus sign.
              assert np.linalg.norm(np.abs(UpperCAmelCase_					) - np.abs(UpperCAmelCase_					)					) <= 1E-6


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      test_power_iteration()





